Deflection of Slabs

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Check Deflection of Slabs for BS 8110 Part 1

Method of checking the deflection of the slabs are similar to the checks of beam deflection. Checking slab deflection is included in the beam design section of BS 8110 Part 01.

Deflection can be checked by two methods. If you know the maximum deflection for relevant load case, we can check whether it is with in the limit. Code gives the maximum limits of deflections base on the spans.

Other method of check the deflection is that limiting the basic span over effective depth ratio to certain values give in the table 3.9 of BS 8110 Part 01 1997.

Following table shows the basis span over depth ratios for rectangular section and flange sections.

Depending on the type of the slab boundary condition, span over depth ratio is selected from above table. For example, if slab is simply supported, we select 20 as the basic span over depth ratio.

The values give in the above table can be modified by multiplying the factors found for tension reinforcements, compression reinforcements and for deflections due to the creep and shrinkage. Normally factor for creep and shrinkage is not apply.

Modification factor for tension reinforcements can be found from the table 3.10 of BS 8110 Part 01.
See the following figure.

If we know the service stress and the bending stress, we can directly find the modification factor from above table or we can use the equations give bellow the table to calculate the modification factor.

Modification factor for compression reinforcement can be found form the table 3.11 of BS 8110 Part 01 1997.

If we provide compression reinforcement, can multiply by this factor and otherwise the factor is considered as 01 where we do not provide compression reinforcements.

Example

Data

Effective depth               = 120 mm
Reinforcement required  = 197 mm2
Reinforcement provided = 393 mm2
Span                                = 3000 mm 
Bending Moment            = 4.8 kNm
Steel strength                  = 460 N/mm2

No compression reinforcement is provide
Consider a simply supported slab for this example

Allowable span/ depth     = 20

Find modification factor for tension reinforcements

since we know the characteristic strength of the steel, required reinforcement area and the provided reinforcement area, we can calculated the design service stress (fs) for the equation given bellow the table 3.10.

f s                                     = 2x460x197 / (3x393)
                                         = 153.7 N/mm2

for the equation give bellow the table 3.10, modification factor can be found.

Modification factor          = [ 0.55 + (477 - 153.7) / { 120(0.9 + 0.33) ] ≤ 2
                                         = 2.19 > 2

Hence, modification factor is 2.

Allowable span/ depth ration   = 20 x 2
                                                  = 40

Actual span / depth ratio           = 3000 / 120
                                                  = 25

Allowable span over depth ratio is grater than the actual span over depth ratio.
Hence, deflection is OK.

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